The Bloodthirster vs Last Whisper

DiffTheEnder bringing you the latest mathematical analysis here, and I've got an analysis that may cause some of you to change up your build.

Without any delay, today's analysis:

The Bloodthirster vs Last Whisper as the 3rd item

As the title implies, this is oriented towards the AD carry role and their build path. To better understand the direction and aim of today's analysis, a background/crash course in the standard AD carry build is needed.

Baby Steps

Your standard ADC goes bot-lane with a support and in most scenarios builds the following items, with slight variations in order depending on how the lane is going.

Now here's where things get interesting. What do you build next?

The higher skilled players will most likely be answering with, "a Last Whisper or some defence", while the lower Elo players might answer with "The Bloodthirster". One of my friends once said, "Building Last Whisper before The Bloodthirster is a free 100 Elo" - I was intrigued. Could the difference really be that significant?

Well, needless to say, I pulled out the formula and the math is shown below.

The video version can be seen here:

Read on for the full article!

Assumptions

Since we're interested in a 3rd item analysis - assumptions have to be made about what set-up the AD carry has at the time of finishing the 3rd item.

These are the assumptions I used.

- The champion will be at level 18

- With the following mastery set up

and a rune set up similar to this:

and that at the time of finishing the 3rd item, they will have an Infinity Edge and a Doran's Blade as added damage items (Phantom Dancer as well, but that doesn't give attack damage).

Depending on the AD carry in question, the Attack Damage of the champion at this point may range anywhere from 210 to 225AD. In terms of the results of the calculation, the variation is not huge and therefore a flat value of 215 AD can be assumed to represent accurate values for AD carries. I'm taking a lower bound for the AD since you may be building the Last Whisper pre-18 if it's a good game.

The Comparison in Question

So what exactly do we need to be comparing? The biggest purpose of both items is to maximise your damage output.

Last Whisper does this by giving you a decent amount of attack damage and the ability to penetrate a lot of your enemy's armor.

The Bloodthirster does this by giving you huge amounts of attack damage and a return of life for every hit. The comparison can be thought of as a sharp dagger vs. a blunt hammer (that somehow heals you).

There is one key factor (among a variety of others) in the comparison that decides which item is better to buy - the enemy's armor.

The more armor the enemy has, the more effective the sharp dagger of a Last Whisper is. The comparison is a question of, "At what enemy armor values does 40AD 46%/6 ArP outdo 60-100AD and 10%/6 ArP?".

Fear not. Results are here.

The Almighty Graph

Let me try to explain the best way to read this graph.

If you have an Infinity Edge, a Doran's Blade, full AD marks/Quints and full 21 in offence and you are at level 18 (giving you a total value of ~215 AD) and are considering whether to buy a LW or BT next - take a look at this graph.

- If the enemy has more than 30 armor, a Last Whisper outdoes a fresh Bloodthirster.

- If the enemy has more than 107 armor, a Last Whisper outdoes a fully stacked Bloodthirster.

Where did I get 30 and 107 from? Look at where the line intercepts the 'Damage Required' values of 60 and 100 (which are the values of an empty/full Bloodthirster).

For those of you who think the 215 AD value may be too high, do not fret, for changing it to a value like 180 AD, gives you values of 36-135 as opposed to 30-107. The variations are not huge is the point to take away and the conclusions I will make are accurate :)

Information to be gained

From the graph, it can be seen that at any value greater than 107 armor, the Last Whisper clearly exceeds the Bloodthirster whether it be stacked or not. Now this begs the question, what armor values are the enemy likely to have at this point. Considering that you are at the latter parts of the game and will be building the Last Whisper at any time from level 15-18 depending on how fed you are, it only makes sense to apply the values for the times when the enemy is at the latter parts of the game as well.

At 60 armor, you would require ~78AD to equal the damage from a Last Whisper, which is a half stacked Bloodthirster - and this is for a level 18 Heimerdinger with no armor runes/masteries.

However this is an unlikely situation as the enemy will likely have at least an Aegis of the Legion if they are half-decent. This gives out an aura of 12 armor to anyone near the item owner. So our squishy Heimerdinger is now at 72 armor and you would need at least 84 damage to equal the output from Last Whisper.

Let's take a look at a more realistic situation vs. an average AD carry who would have ~72 armor at 18, then we add 12 armor from Aegis and 6 armor from masteries and 13 from runes to give a grand total of 103 armor. At this value, you would need a fully stacked Bloodthirster, or to be more accurate 98.48 AD to equal the output from Last Whisper.

These values get increasingly worse when you start looking at tanks who have nearly 200 armor.

It's safe to say that Last Whisper is a better option for basic attacks in pretty much all situations at this point due to the high armor values of enemies.

Critical Strikes

One of the biggest arguments for building a Bloodthirster at this point is that it amplifies critical strike damage much more. 2.5 times 80 is more than 2.5 times 40. I'd just like to say - false. Critical strikes double the final damage and not your AD. So it's not the 80AD that gets multiplied by 2.5 but the final damage value. This means that whether you're striking critically or not, the graph for damage required stays the same as the above.

Life Steal

A major component of The Bloodthirster is the Lifesteal. In all realistic situations, you will heal for more per hit with a Bloodthirster than having a Last Whisper+ Vamp. Scepter. The difference is quite significant. You will heal for anywhere between 20% and 146% more per hit with Bloodthirster depending on how stacked it is and how much armor the enemy has. I find this argument to be pointless however. The Last Whisper costs a full 710 gold less than the Bloodthirster. If Lifesteal is really that important for you at that portion of the game, a second Vampiric Scepter or an Executioner's Calling or even a Zeke's Herald (on a support) can be bought to temporarily have a comparable lifesteal value.

Conclusion

This one line summarises what I think of the Last Whisper vs. The Bloodthirster.

"If the enemy has more than 30 armor, a Last Whisper outdoes a fresh Bloodthirster."

By the time you build a Last Whisper, every teamfight could be the one which decides the game. Farming a Bloodthirster is not the ideal task to be carrying out at this crucial stage of the game. Having shown you all the calculations, I feel 100% safe in saying, always buy a Last Whisper as your third item if it's a choice between the Bloodthirster and Last Whisper.

tl;dr Last Whisper #1

Feel free to disagree - that is my opinion and I am not forcing it down your throat.

As always, I hope you guys enjoyed the analysis. If you are one of those people who couldn't be bothered reading the whole article and scrolled down for the conclusion - maybe the video version will be something you like better!

Cheers,

DiffTheEnder

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Comments

Can you do one of a Phantom Dancer vs. Last Whisper? If you include the IE and Mastery crit damage increase, a PD's crit gives +48% damage on average (30% x 160%), which would seem to do much more damage than a LW.

I was just thinking exactly the same issue. Even though your second PD will probably be a bit less cost-eficient due to mspd cap, I think it's still a better choice unless you're playing against full-armored-bruisers team whatsoever.

I agree with the damage thingy its kinda obviuos, but lifesteal is something that most ad based champions need, and if you need lifesteal, what would you suggest buying instead of bt, because well, most tops can do with a wrigglers, but it just doesnt work as well for late game since it doesnt give neither enough armor or lifesteal or damage. In some cases like, lets say renekton, bloodthirster, or as i like to do my things atmas + infinity work so much better than a last whisper. The comparasing thingy is only meant for aa's which is ussually only the case for carrys, and some of the are very dependant on ad, for example, corkis passive will work much better with bloodthirster than last whisper, or urgot damage will be higher, im not a carry player so i cant say all that much, but from my point of view, Last Whisper - The BloodThirster usefulness is optional, its about the champion not item.

It would again depend on the amount of armor the enemy has. PD would increase overall damage by a flat amount(nothing "scales"), while LW gives damage depending on enemy armor.

Usually infinity edge + zeal + 2dorans is around 25 mins, so enemies usually don't have that much armor yet, (<150). I would probably finish PD, and then get LW or BC. Swap BC for LW when many enemies have over 200 armor.

How do these calculations hold up when you factor in Draven? I've tried experimenting with BT vs. LW, but it's tough to get accurate results when there are so many other variables in a normal game (how fed are you, what other items are people building, etc.) to factor in. Draven's massive AD scaling on autos seems like it would be interesting to take note of or would the conclusion remain the same as the critical strike argument?

Can you please do a Black Cleaver vs Last Whisper comparison. I saw a big maths post on forums on it about 6 months ago and they said that Black Cleaver gives more dps single target than LW on targets below 300 armor. Interesting to see if you find the same thing :).

I was a big part of that discussion, and personally did a lot of the math for that. I found that Black Cleaver did more damage at three stacks of it's debuff, than last whisper, at 230 armor or less. Meaning, against nearly everyone, black cleaver is better. For two stacks, it's like 150 armor, and for one stack it's 100, I think. Something like that.

BUT, of course that means you have to have three stacks. The attack speed on it will help you get stacks on quicker. Keep in mind these numbers are for autoattacks only, and for continued dps, to include the extra attack speed from the black cleaver. For physical damage abilities, and for no-stacked enemies, last whisper is much better.

If you team has a lot of physical damage dealers, black cleaver will significantly amplify your team's damage output. So use your judgement, and consider the following:Do I have multiple physical damage dealers on my team? Do I have an attack speed steroid available, from an ability or support? Do I want to spend a little more money for potentially more damage? If so, buy black cleaver, otherwise, buy last whisper.

It's less about how much armor the enemies have, because normally, only 1 or 2 enemies have anywhere near 200+ armor, and you should be focusing on squishies first if possible, the most important thing with black cleaver is positioning, and getting those stacks on one target and burning them down. If you can do that, even tanks will melt like butter.

Diff already did this post exactly. The results are exactly what you'd think it to be. On average, if you are attacking the same person 3 times or more, BC is better. If you are not (you usually have to switch targets as an AD carry) or if multiple targets have high amounts of armor (200 or greater, not exact but around there) then you should buy LW.